Throwing out some notes for discussion. Wanting to condense a model of understanding that can allow us to see (and execute) that the applied hand techniques are exactly the same as the striking techniques. Same forces, same axis of operation. All these correspond to the sword movements. It's the same thing.

Would it be accurate to say your referrences of individual axes denote a relatively greater degree of influence? My understanding is that all movement should ideally be operating/strong on all three at the same time (even cuts, which otherwise seem to be planar), but I can see how at different times we might have an axis or two which hold relatively greater power potential...
My understanding is that any whole-body movement should ideally have the ability to issue strikes from any point of the body (more or less) so, from this standpoint, potentially anything (or near enough) can be a strike; the form is somewhat moot.
That said, I really like the similarity between ura ken and sankyo (we often put/strike the sankyo into uke's face before moving on to the pin or a throw). When I think of them as more or less the same thing, it seems to help me get the right feeling.